Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However, recently there have been a number of works demonstrating that these improved algorithms can be “fooled” using specially constructed adversarial examples. In turn, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks.

In this talk I will describe a recently proposed variational framework for understanding adversarial robustness. This variational problem has deep connections with optimal transportation, isoperimetric problems, and mean curvature flow. I’ll discuss some of our recent results which make these connections and establish a delicate regularity theory for optimal solutions to this problem. I’ll also discuss recent algorithmic advances which can detect and track topological changes that are induced by the presence of an adversary in the variational problem.

Zoom meeting: Link